Evaluating the Accuracy of Small P-Values In Genetic Association Studies Using Edgeworth Expansions

Gang Zheng; Jinghong Xiong; Qizhai Li; Jinfeng Xu; Ao Yuan; Joe L. Gastwirth

doi:10.1111/sjos.12283

Evaluating the Accuracy of Small P-Values In Genetic Association Studies Using Edgeworth Expansions

Gang Zheng, Jinghong Xiong, Qizhai Li, Jinfeng Xu, Ao Yuan^*, Joe L. Gastwirth

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

1 Citation (Scopus)

Abstract

The asymptotic distributions of many classical test statistics are normal. The resulting approximations are often accurate for commonly used significance levels, 0.05 or 0.01. In genome-wide association studies, however, the significance level can be as low as 1×10⁻⁷, and the accuracy of the p-values can be challenging. We study the accuracies of these small p-values are using two-term Edgeworth expansions for three commonly used test statistics in GWAS. These tests have nuisance parameters not defined under the null hypothesis but estimable. We derive results for this general form of testing statistics using Edgeworth expansions, and find that the commonly used score test, maximin efficiency robust test and the chi-squared test are second order accurate in the presence of the nuisance parameter, justifying the use of the p-values obtained from these tests in the genome-wide association studies.

Original language	English
Pages (from-to)	1-33
Journal	Scandinavian Journal of Statistics
Volume	45
Issue number	1
DOIs	https://doi.org/10.1111/sjos.12283
Publication status	Published - 1 Mar 2018
Externally published	Yes

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

chi-squared test
Edgeworth expansion
maximin efficiency robust test (MERT)
maximum likelihood estimate
nuisance parameter

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abstract = "The asymptotic distributions of many classical test statistics are normal. The resulting approximations are often accurate for commonly used significance levels, 0.05 or 0.01. In genome-wide association studies, however, the significance level can be as low as 1×10−7, and the accuracy of the p-values can be challenging. We study the accuracies of these small p-values are using two-term Edgeworth expansions for three commonly used test statistics in GWAS. These tests have nuisance parameters not defined under the null hypothesis but estimable. We derive results for this general form of testing statistics using Edgeworth expansions, and find that the commonly used score test, maximin efficiency robust test and the chi-squared test are second order accurate in the presence of the nuisance parameter, justifying the use of the p-values obtained from these tests in the genome-wide association studies.",

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AU - Li, Qizhai

AU - Xu, Jinfeng

AU - Yuan, Ao

AU - Gastwirth, Joe L.

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - The asymptotic distributions of many classical test statistics are normal. The resulting approximations are often accurate for commonly used significance levels, 0.05 or 0.01. In genome-wide association studies, however, the significance level can be as low as 1×10−7, and the accuracy of the p-values can be challenging. We study the accuracies of these small p-values are using two-term Edgeworth expansions for three commonly used test statistics in GWAS. These tests have nuisance parameters not defined under the null hypothesis but estimable. We derive results for this general form of testing statistics using Edgeworth expansions, and find that the commonly used score test, maximin efficiency robust test and the chi-squared test are second order accurate in the presence of the nuisance parameter, justifying the use of the p-values obtained from these tests in the genome-wide association studies.

AB - The asymptotic distributions of many classical test statistics are normal. The resulting approximations are often accurate for commonly used significance levels, 0.05 or 0.01. In genome-wide association studies, however, the significance level can be as low as 1×10−7, and the accuracy of the p-values can be challenging. We study the accuracies of these small p-values are using two-term Edgeworth expansions for three commonly used test statistics in GWAS. These tests have nuisance parameters not defined under the null hypothesis but estimable. We derive results for this general form of testing statistics using Edgeworth expansions, and find that the commonly used score test, maximin efficiency robust test and the chi-squared test are second order accurate in the presence of the nuisance parameter, justifying the use of the p-values obtained from these tests in the genome-wide association studies.

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KW - Edgeworth expansion

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JF - Scandinavian Journal of Statistics

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Evaluating the Accuracy of Small P-Values In Genetic Association Studies Using Edgeworth Expansions

Abstract

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Research Keywords

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